Just making this question in case someone encounter the same problem, I will answer it.
So I just bought an ebook for my Kindle in amazon, because some circumstances I have not WIFI available in my house as many other times, therefore I want to dowload it to my PC and transfer it to my Kindle via USB cable, as many other times.
I go to the page where you handle all your ebooks (sorry but I'm not a native english speaker, so I don't know the exact names in english version of amazon web... if you know them, you are officially invited to edit the question :), locate my new ebook, hit the "..." button, select the option to download the ebook and transfer ir via USB and select my kindle in the dropdown menu.
And nothing happens.
Seconds later, suddenly a message appear and dissappear in screen, saying something like "Download your book from My multimedia library" (again, not english native speaker), but the book doesn't get downloaded and I can't for my life find the above mentioned library.
So, I don't have the book, and it seems that the library doesn't exist.